While the Ferrari's new front wing continued to prompt distinctive showers of sparks as it vibrated again the track surface, the revised car showed promising pace, with Massa lapping the dusty track in 1m25.706s 18 minutes before the end of the session to claim the top spot.
His team-mate Fernando Alonso also showed well in third, 0.224 seconds off Massa's pace.
They were split by champion Sebastian Vettel, whose Red Bull had been quickest for the majority of the afternoon, until Massa's fast time saw the German pipped by 0.088s.
Morning pacesetter Lewis Hamilton, who will go into qualifying for a three-place grid penalty for disregarding yellow flags earlier today, was fourth quickest in the best of the McLarens, with his team-mate Jenson Button sixth behind Mark Webber's Red Bull.
Force India took 'best of the rest' honours in front of its effective home crowd thanks to Adrian Sutil's seventh place, two positions ahead of team-mate Paul di Resta, as they sandwiched Bruno Senna's Renault. SebastienBuemi completed the top 10 for Toro Rosso.
The Mercedes were further back than usual in 19th (NicoRosberg) and 21st (Michael Schumacher) - the seven-time champion having missed some of the session while an issue was resolved on his car.
There were plenty of small incidents as the drivers explored the track's limits, particularly at Turn 6, and one red flag after Jerome D'Ambrosio went off at Turn 11 and ended up backed his Virgin into the barriers, causing significant damage. He was unhurt and the session quickly resumed.
Petrov also had a spin in his Renault, while Pastor Maldonado dumped his Williams in the Turn 9 gravel early on but was retrieved in time to rejoin the session and complete 24 laps.
1m25.794s + 0.088
1m25.930s + 0.224
1m26.454s + 0.748
1m26.500s + 0.794
1m26.714s + 1.008
1m27.316s + 1.610
1m27.498s + 1.792
Paul di Resta
1m27.853s + 2.147
1m27.868s + 2.162
1m27.890s + 2.184
1m28.050s + 2.344
1m28.289s + 2.583
1m28.552s + 2.846
1m28.691s + 2.985
1m28.708s + 3.002
1m29.332s + 3.626
1m30.241s + 4.535
1m31.098s + 5.392
1m31.469s + 5.763
1m31.804s + 6.098
1m32.768s + 7.062
1m32.824s + 7.118
Story source: Autosport.com
Read: Hamilton fastest in first free practice
Watch: Indian Grand Prix, Friday in pictures
Issue: 198 | Autocar India: February 2016
Access member only content, take part in discussions with comments on blogs, news and reviews and receive all the latest news and reviews straight to your inbox. Join now for free.
Processing registration... Please wait.
This process can take up to a minute to complete.
A confirmation email has been sent to your email address - SUPPLIED EMAIL HERE. Please click on the link in the email to verify your email address. You need to verify your email before you can start posting.
If you do not receive your confirmation email within the next few minutes, it may be because the email has been captured by a junk mail filter. Please ensure you add the domain @autocarindia.com to your white-listed senders.